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• The model allocates safety stocks in supply chains at minimum cost. • An MIQCP reformulation with piecewise approximation greatly improves computational efficiency. • The piecewise function yields an improved estimation for the fill rates. • The GSM is extended to handle non-normally distributed demands. • Real-world case studies solved to optimality within few seconds of computational time. This paper presents a Multi-Echelon Inventory Optimization (MEIO) framework, based on the Guaranteed-Service Model (GSM), to allocate safety stocks across a supply chain with several locations and products, minimizing costs while meeting service level objectives. Extending previous work by Achkar et al. (2023), this paper enhances the Mixed-Integer Quadratically Constrained Program (MIQCP) with a highly efficient solution approach. The model introduces a piecewise linear approximation, significantly improving computational efficiency and the accuracy of the approximation for the fill rate function. It also introduces a different and more efficient approach to account for stochastic lead times using a discrete function. Moreover, an extension of the approach to account for non-normally distributed demands is proposed. The model is applied to several instances of a real-world case study from a pharmaceutical company, with more than 7300 product-location combinations, showing that optimal solutions can be obtained within few seconds of computational time. [ABSTRACT FROM AUTHOR]

• We develop a mathematical programming model for scheduling turnaround maintenance activities for a network of plants in a supply chain. • We propose a heuristic algorithm for solving the model when the network has large number of plants. • A case study petrochemical supply chain is used to demonstrate the utilization of the model and the effectiveness of the heuristic. Turnaround (TAM) is a periodic maintenance in which plants are shutdown to conduct inspections, repairs, preventive maintenance and overhauls. The shutdown periods range from three to four weeks and prolonging this period is expensive and therefore requires effective planning. The primary purpose of this paper is to develop a mathematical programming model to coordinate and plan TAM for several plants in an integrated supply chain network. A secondary objective is to develop a heuristic algorithm for solving the model when the network has large number of plants. The model and the algorithm are developed, tested and applied on a case study petrochemical supply chain. The exact algorithm takes 8.3 times the time of the heuristic. In addition the heuristic algorithm provides near optimal solution in much shorter time. The developed model provides a tool to plan TAM for several plants in an integrated supply in an optimal fashion. [ABSTRACT FROM AUTHOR]

• Comprehensive review of mathematical programming models for shale oil & gas development. • Detailed comparison of publications in five major topic areas: (1) development planning, (2) water management, (3) production optimization, (4) supplies, gathering & processing, and (5) LCA & sustainability. • Highlight of optimization deployment success stories in industry (i.e., optimization value proposition in oil & gas). • Perspective on outstanding research opportunities in the respective field of study. In this paper, we provide a comprehensive review of mathematical programming models for shale oil & gas development, and we offer a perspective on outstanding research opportunities. We distinguish contributions in five major topic areas, namely: (1) development planning, (2) water management, (3) production optimization, (4) supplies, gathering & processing, and (5) life cycle analysis & sustainability. We highlight how various types of mathematical programming models (i.e., linear programs, nonlinear programs, mixed-integer linear programs, mixed-integer nonlinear programs) have been proposed primarily by the Process Systems Engineering community to address the respective decision-making problems, and we highlight instances of successful deployment in industry. Finally, based on a critical assessment of the existing body of work, we identify opportunities for future research across the major topic areas. [ABSTRACT FROM AUTHOR]

Highlights • A new rigorous bilevel decomposition strategy for MILPs with strong linking constraints. • An extended cross decomposition method based on the bilevel decomposition strategy. • Application of the extended cross decomposition method to stochastic programming with CVaR constraints. • Case studies with a variety of scenario instances showing significant computational advantages of the proposed methods. Abstract Large-scale mixed-integer linear programming (MILP) problems, such as those from two-stage stochastic programming, usually have a decomposable structure that can be exploited to design efficient optimization methods. Classical Benders decomposition can solve MILPs with weak linking constraints (which are decomposable when linking variables are fixed) but not strong linking constraints (which are not decomposable even when linking variables are fixed). In this paper, we first propose a new rigorous bilevel decomposition strategy for solving MILPs with strong and weak linking constraints, then extend a recently developed cross decomposition method based on this strategy. We also show how to apply the extended cross decomposition method to two-stage stochastic programming problems with conditional-value-at-risk (CVaR) constraints. In the case studies, we demonstrate the significant computational advantage of the proposed extended cross decomposition method as well as the benefit of including CVaR constraints in stochastic programming. [ABSTRACT FROM AUTHOR]

In today's business world, oil companies cannot be productive and competitive, and thus, will not survive without taking the supply chain management concepts into account. Consequently, the management of a crude oil supply chain (COSC) is increasingly receiving substantial importance. The growing number of papers and books on this topic is a further witness of this fact. To foster insight into issues intertwined with COSC problems, this paper is devoted to an extensive review of mathematical programming models in this context. The classification approach for this review is based on a taxonomy framework. In this framework, ongoing and emerging challenges surrounding the strategic and tactical decisions of COSC problems are investigated. As a main goal, the gaps of literature are analyzed to recommend possible research directions. [ABSTRACT FROM AUTHOR]

This paper presents a new step-wise sequential solution strategy for the synthesis of heat integrated water networks (HIWNs) comprising of two mathematical models. The first model minimizes water and energy costs. The optimal freshwater and water flow rates within the HIWN are determined from this model. Using these optimal flow rates, different configurations of HIWN are evaluated for the purpose of heat integration. The second model is the stage-wise heat exchanger network (Yee and Grossmann, 1990), which is solved for each of the evaluated network configuration in a sequential manner. Using this proposed strategy, a set of locally optimal HIWNs are produced and the best one is chosen based on the minimum total annual cost (TAC). The proposed sequential strategy is applied to small and medium sized examples in the literature. The results show that the proposed new sequential solution strategy can be successfully applied to small and medium sized HIWN problems. [ABSTRACT FROM AUTHOR]

Over the last few decades, research on resource constrained project scheduling has focused on the development of mathematical programming based approaches for the generation of a nominal schedule under a deterministic environment. During the implementation phase, however, the nominal schedule may need to be revised when one or more resources are disrupted for a length of time. In this paper, we formulate two discrete time based models to deal with two different disruption scenarios for multi-mode resource constrained problems. We propose a reactive re-scheduling procedure for a single, as well as a series of disruptions, without having any disruption information in advance. To test the proposed approaches, sets of ten, twenty and thirty-activity multi-mode test instances from Project Scheduling Library (PSLIB) were used after introducing randomly generated disruption events. The experimental studies were also carried out to determine the effect of different factors related to the disruption recovery process. [ABSTRACT FROM AUTHOR]

Safety and performance are important factors in the design and operation of chemical plants. This paper describes the formulation of a mixed integer nonlinear programming model for the optimization of plant layout with safety considerations. The model considers a quantitative risk analysis to take safety into account, and a bowtie analysis is used to identify possible catastrophic outcomes. These effects are quantified through consequence analyses and probit models. The model allows the location of facilities at any available point, an advantage over grid-based models. Two case studies are solved to show the applicability of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new mathematical programming model for the optimal synthesis of recycle and reuse networks considering simultaneously the integration of the water network system and the surrounding watershed to satisfy process and environmental constraints. The model considers the optimal location of the new industrial facility to integrate its wastewater discharge to the environment with the surrounding watershed through a disjunctive formulation. The pollutants discharged for the new plant are tracked simultaneously with the other discharges to the watershed (i.e., residential, sanitary, industrial and extractions), and the natural phenomena that affect the composition of the watershed (i.e., evaporation, filtration, etc.), in addition to the chemical reactions that are carried out in the rivers. The objective function consists in minimizing the total annual cost that is constituted by the installation of the new plant cost (including the transportation for raw materials, products and services, as well as the land cost), the wastewater treatment costs (including the piping cost) and the fresh sources cost. Two example problems were used to show the applicability of the proposed methodology. [Copyright &y& Elsevier]

Abstract: A new simplified scalable mathematical model, based on concepts of stream analysis, temperature paths and internal heat exchange, has been developed for synthesis of a multiple effect evaporator systems. In this model, fresh feed is assumed to be composed of product and number of condensate streams, which come out from different effects and these are treated as separate streams. For the present work a septuple effect flat falling film evaporator system, used for concentrating black liquor in an Indian Kraft Pulp and Paper mill, has been considered. This system is being operated under backward sequence with condensate-, feed- and product-flashing as well as steam splitting in first two effects. The set of linear algebraic equations for this model are self-generated through programming and is solved simultaneously using Gaussian Elimination Method with partial pivoting. Results of the present approach are validated with published model and industrial data. [Copyright &y& Elsevier]

Abstract: An overview of an iterative and sequential methodology, called the Sequential Framework for heat exchanger network synthesis (HENS), is presented in the paper. The main objective of the Sequential Framework is to solve industrial size problems. The subtasks of the design process are solved sequentially using mathematical programming. There are two main advantages of the methodology. First, the design procedure is, to a large extent, automated while keeping significant user interaction. Second, the subtasks of the framework (MILP and NLP problems) are much easier to solve numerically than the MINLP models that have been suggested for HENS. One of the limiting factors in the methodology is related to the two MILP models where significant improvements are required to prevent combinatorial explosion. To ease this problem for the minimum number of units MILP sub-problem, two different approaches to the issue were studied. The minimum number of units problem is modified to reduce the gap using physical insights and heuristics. Another novel approach tested was to reformulate some parts of the model by use of some ideas from set partitioning problems. Results show that though both methods succeed in tightening the LP relaxation, the model solution times remain too long to be of interest in the Sequential Framework. [Copyright &y& Elsevier]

Abstract: Sustainability has recently emerged as a key issue in process systems engineering (PSE). Mathematical programming techniques offer a general modeling framework for including environmental concerns in the synthesis and planning of chemical processes. In this paper, we review major contributions in process synthesis and supply chain management, highlighting the main optimization approaches that are available, including the handling of uncertainty and the multi-objective optimization of economic and environmental objectives. Finally, we discuss challenges and opportunities identified in the area. [Copyright &y& Elsevier]

Abstract: Extended mathematical programs are collections of functions and variables joined together using specific optimization and complementarity primitives. This paper outlines a mechanism to describe such an extended mathematical program by means of annotating the existing relationships within a model to facilitate higher level structure identification. The structures, which often involve constraints on the solution sets of other models or complementarity relationships, can be exploited by modern large scale mathematical programming algorithms for efficient solution. A specific implementation of this framework is outlined that communicates structure from the GAMS modeling system to appropriate solvers in a computationally beneficial manner. Example applications are taken from chemical engineering. [Copyright &y& Elsevier]

Abstract: In this paper, mathematical programming coupled with superstructure is utilized to optimize regeneration recycling water networks at the stage of grass-roots design. The optimization is virtually a multi-objective problem with several important parameters on regeneration recycling involved. Considering the relative importance of these parameters, sequential optimization is adopted to solve this multi-objective problem. Freshwater consumption, regenerated water flowrate and contaminant regeneration load, are in turn minimized, which correspond to three mathematical models. By solving these models step by step, a regeneration recycling water network can be constructed, which is economically favorable in terms of qualitative analysis. The complexity of water network configuration is also taken into account by minimizing the number of interconnections among processes. Additionally several examples are used to demonstrate the application of the proposed methodology. In comparison with the available technologies, the proposed methodology excels in simplicity and adaptability for grass-roots design by exempting from complicated and variable economic parameters. [Copyright &y& Elsevier]